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1 year ago

The null space of a is the solution set of the equation ax = 0. a. true b. false

Mathematics

1 answer:

horrorfan [7]1 year ago

7 0

It is true that the null space of a is the solution set of the equation ax = 0.

<h3>What is the proof?</h3>

The null space of a matrix A is Nul(A)= {x : Ax=0}. In other words, if A is m × n, then its null space consists of those vectors x ∈ Rn which solve the homogeneous equation Ax= 0.

Solving Ax=0 yields an explicit description of Nul(A).

Therefore, the Option A is correct.

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0. © MP.2 Reasoning A teacher noticed 5/8

djyliett [7]

Answer:

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Step-by-step explanation:

3 0

2 years ago

Can someone help me with this problem

Naily [24]

<h3>Answer: Choice A</h3><h3>The point Z ' is at (8,4)</h3><h3>The point Y ' is at (0,4)</h3>

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Explanation:

The key thing here is that point Z does not move. Why not? Because this is where the center of dilation occurs. The center point is fixed. Everything around the center will expand away from, or contract toward, the center.

In this case, the scale factor is 4/5 = 0.8 which is less than 1. So points will contract toward the center. The old pre-image shrinks to make the image smaller.

Note how point Y = (-2,4) is 10 units away from point Z. You can count out the spaces or subtract the x coordinates. Use an absolute value to make sure the result is positive

|x1-x2| = |-2-8| = |-10| = 10

|x2-x1| = |8-(-2)| = |8+2| = |10| = 10

So 0.8 times this distance is therefore 0.8*10 = 8 meaning that point Y' is going to be 8 units away from point Z' or Z.

Subtract 8 from the x coordinate of point Z to get x-8 = 8-8 = 0.

The y coordinate stays the same at y = 4 the whole time.

----------------------------------------

In short, point Y starts at (-2,4) and moves to (0,4)

Distance from Y to Z is 10 units

Distance from Y' to Z' is 8 units

8/10 = 4/5 = 0.8 is the scale factor

Point Z does not move. So Z and Z' are at the same location.

5 0

3 years ago

Read 2 more answers

Nathan has a sculpture in the shape of a pyramid. The height of the sculpture is 3 centimeters less than the side length, x, of

uysha [10]

Let
x-----------> <span>the side length of a pyramid square base
h-----------> t</span>he height of the sculpture <span>in the shape of a pyramid

we know that
h=(x-3)
Volume=162 cm</span>³
Volume=x² *(x-3)/3
then
x² *(x-3)/3=162----------> x³-3x²=486----------> x³-3x²-486=0
x³-3x²-486=0-------- <span>this equation can be used to find the length of the sculpture’s base

using a graph tool-----------> </span>to find the solution
x=9 cm -------------> see the attached figure
h=(x-3)-----> h=9-3--------> h=6 cm

the answer is
<span>the length of the sculpture’s base is 9 cm
</span>the height of the sculpture is 6 cm

8 0

3 years ago

Water erupting from geyser can reach a temperature of 244 F . The average temperature in Yellowstone National Park is 35F . Use

stiv31 [10]

Difference means subtraction , 244 - 35 = 209
I forgot how to do this problem it was 63 years ago

4 0

3 years ago

HELP ME PLEASE!

Delicious77 [7]

Sounds as tho' you have an isosceles triangle (a triangle with 2 equal sides). If this triangle is also a right triangle (with one 90-degree angle), then the side lengths MUST satisfy the Pythagorean Theorem.

Let's see whether they do.

8^2 + 8^2 = 11^2 ???
64 + 64 = 121? NO. This is not a right triangle.

If you really do have 2 sides that are both of length 8, and you really do have a right triangle, then:

8^2 + 8^2 = d^2, where d=hypotenuse. Then 64+64 = d^2, and

d = sqrt(128) = sqrt(8*16) = 4sqrt(8) = 4*2*sqrt(2) = 8sqrt(2) = 11.3.

11 is close to 11.3, but still, this triangle cannot really have 2 sides of length 8 and one side of length 11.

7 0

2 years ago